A001466 Denominators of greedy Egyptian fraction expansion of Pi - 3.
8, 61, 5020, 128541455, 162924332716605980, 28783052231699298507846309644849796, 871295615653899563300996782209332544845605756266650946342214549769447
Offset: 1
Examples
Pi - 3 = 1/8 + 1/61 + 1/5020 + 1/128541455 + ... .
References
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Simon Plouffe, Table of n, a(n) for n = 1..10 (There is a limit of about 1000 digits on the size of numbers in b-files)
- Mohammad K. Azarian, An Expression for Pi, Problem #870, College Mathematics Journal, Vol. 39, No. 1, January 2008, p. 66. Solution appeared in Vol. 40, No. 1, January 2009, pp. 62-64.
- K. R. R. Gandhi, Edifice of the real numbers by alternating series, International Journal of Mathematical Archive-3(9), 2012, 3277-3280. - From _N. J. A. Sloane_, Jan 02 2013
- Simon Plouffe, Table of n, a(n) for n = 1..14
- H. P. Robinson, Letter to N. J. A. Sloane, Sep 1975
- H. E. Salzer, The approximation of numbers as sums of reciprocals, Amer. Math. Monthly, 54 (1947), 135-142.
- Eric Weisstein's World of Mathematics, Egyptian Fraction
- Wikipedia, Greedy algorithm for Egyptian fractions
- J. W. Wrench, Jr., Letter to N. J. A. Sloane, Mar 27 1974
- Index entries for sequences related to the number Pi
Programs
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Mathematica
lst={};k=N[(Pi-3),1000];Do[s=Ceiling[1/k];AppendTo[lst,s];k=k-1/s,{n,12}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 02 2009 *) -
PARI
x = Pi - 3; f(x, k) = if(k<1, x, f(x, k - 1) - 1/n(x, k)); n(x, k) = ceil(1/f(x, k - 1)); for(k = 1, 7, print1(n(x, k), ", ")) \\ Indranil Ghosh, Mar 27 2017
Comments